It is advisable to describe an optical system that captures the image, of a three-dimensional object, as a process of transfer between planes. By using an optical system, only one plane of the object is well focalized on the plane in which the image is detected. The other planes of the object are not well focalized on the plane where the image is detected. It is common to indicate that for the other planes of the object, the optical system suffers from focalization errors.
The tolerance with which the optical system is able to capture the other levels of the object, is called depth of field, which is controlled by opening or closing the opening of the pupil of the optical system. Closing the pupil results in a larger depth of field. However, closing the pupil also reduces the resolution and the luminous capture of the optical system, as described in Leo Levi, Applied Optics: A Guide to Optical System Design/Volume I. (Wiley, 1968) ISBN-10: 0471531103. In order to preserve the resolution and luminous capture of the optical system it is necessary to find a new method for depth of field control.
In the past two decades, several devices were designed to maintain high resolution and extend the depth of field, moderately and selectively easing some parts of the pupil. See for example the publication “Improvement in the OTF of a Defocused Optical System Through the Use of Shade Aperture,” Appl. Opt. 10, 2219 (1971) J. Ojeda-Castaneda, L R Berriel-Valdes, and E. Montes, “Line Spread Function Relatively Insensitive to Defocus,” Opt. Lett. 8.458 (1983); G. Indebetow and H. Bai, “Imaging with Fresnel Zone Pupils Masks: Extended Depth of Field,” Appl. Opt. 23, 4299 (1984) J. Ojeda-Castaneda, L R Berriel-Valdes, and E. Montes, “Spatial Filter for Increasing the Depth of Focus,” Opt. Lett. 10, 520 (1985) J. Ojeda-Castaneda, P. Andres, and A. Diaz, “Annular Apodized for Low Sensitivity to Defocus and to Spherical Aberration,” Opt. Lett. 11, 487 (1986). These designs lead to the conclusion that to maintain a pre-specified resolution, it is possible to form images of various planes of the object, but the cosine variations (in other planes of the object) are formed with attenuated amplitude. Consequently, there must be several families of lenses that (for a pre-specified resolution) extend depth of field with images showing cosine variations with low amplitude. Since these images only require a boost in its amplitude, this is accomplished using restoration algorithms known in the technique.
From these last findings, to extend depth of field, new designs are intended to reduce the influence of the focalization errors, thus avoiding cosine amplitude variations being zero. Once the images are captured, the amplitude is restored with algorithms known in the technique, as discussed in patents U.S. Pat. Nos. 6,927,922 and 7,218,448.
To find a new method of depth of field control, it is advisable to mathematically model the image forming optical system as a linear system, see e.g. the book “Introduction to Fourier Optics” by Joseph W. Goodman (McGraw-Hill, 1996), ISBN-10: 0070242542.
A linear model is represented by an optical transference function. The optical transference function module is the function of the modulation transference. This new function specifies with which new amplitude the starting amplitude of a cosine variation which is localized in one of the object's plane is detected (in the image plane). The transference function of the modulation specifies the amplitude transference for each frequency of the cosine variation, and is therefore useful to represent the quality of an optic system, and there relies the convenience to evaluate that function. For this purpose the mathematical operation of autocorrelation of the generalized pupil function is performed, which describes the transmittance in complex amplitude of the optic system. The generalized pupil function is a complex one, which results from multiplying the real function which represents the physical pupil aperture by the transmittance in complex amplitude of the optic filter, which is localized on top of the pupil aperture. In a conventional system, the transmittance in complex amplitude of the optic filter equals one. However, in order to improve the modulation transference function, and consequently improve the quality of the image, it is necessary to modify the transmittance in complex amplitude of the optic filter, as shown in: J. Ojeda-Castaneda and L. R. Berriel-Valdos, “Arbitrarily high focal depth with finite apertures,” Opt. Lett. 13, 183-185 (1988); “Zone plate for arbitrarily high focal depth”, J. Ojeda-Castañeda and L. R. Berriel-Valdos, Applied Optics, Vol. 29, No. 7, pp. 994-997 (1990).
To take into account the influence of the focalization errors it is necessary to incorporate a quadratic phase factor in the coordinates of the pupil. In the latter case, it is convenient to use the mathematical formalism of the function of ambiguity, associated with complex amplitude transmittance of optical filter. The mathematical formalism of the function of ambiguity to identify the complex amplitude transmittance optical filter is less sensitive to focalization errors, as discussed in J. Ojeda-Castaneda, L R Berriel-Valdes, and E. Montes, “Ambiguity function as a design tool for high focal depth, ” Appl. Opt. 27, 790-795 (1988).
To reduce the impact of the focalization errors, without affecting the resolution and luminous capture of the optical system, a transmittance in complex amplitude is searched which is only a function only of the phase. A transmittance in complex amplitude that reduces the impact of focalization error, is able to extend the depth of field to a specific value, which is determined by the maximum difference in optical path introduced by the optical filter as described in the patent U.S. Pat. No. 5,748,371 and in publications ER Dowski and TW Cathey, “Extended depth of field-through wave-front coding,” Appl. Opt. 34, 1859-1865 (1995); A. Sauceda and J. Ojeda-Castaneda, “High focal depth with fractional-power wave Fronts,” Opt. Lett. 29, 560-562 (2004); A. Castro and J. Ojeda-Castaneda, “Asymmetric phase masks for extended depth of field,” Appl. Opt. 43, 3474-3479 (2004); A. Castro, J. Ojeda-Castaneda, and AW Lohmann, “Bow-tie effect: differential operator,” Appl. Opt. 45, 7878-7884 (2006).
U.S. Pat. No. 5,748,371 describes a method to extend depth of field to a specific value using only one lens. In the present invention a method to extend the depth of field in a controlled manner from a minimum to a maximum value using a pair of glasses is protected. This is possible by varying, in a controlled manner, the optical path difference that the proposed lens is capable of generating.
One possible way to vary, in a controlled manner, the difference in optical path, is applying the methodology described in the patent U.S. Pat. No. 3,305,294, which describes a method to vary optical power by the lateral displacement between two lenses, which have a profile that varies as a cubic polynomial.
Unlike U.S. Pat. No. 3,305,294, in the present invention, a method to vary depth of field is protected, while in U.S. Pat. No. 3,305,294, a method to vary optical power is described.
In other words, the present invention describes a method to vary depth of field extension in a controlled way, while in U.S. Pat. No. 5,748,371 depth of field extension is constant. The present invention describes a method to extend depth of field, while in U.S. Pat. No. 3,305,294 a method for varying optical power is described.